A mass transport model with a simple non-factorized steady-state distribution

Abstract

We study a mass transport model on a ring with a sublattice-parallel update, where a continuous mass is randomly redistributed along distinct links of the lattice. The redistribution process on a given link depends on the masses on both sites, in contrast to the zero range process and its continuous mass generalizations. We show that the steady-state distribution takes a simple non-factorized form that can be written as a sum of two inhomogeneous product measures. A factorized measure is recovered for symmetric mass redistribution, corresponding to an equilibrium process. A non-equilibrium free energy can be explicitly defined by the partition function. For a certain class of transition rates, a condensation transition is obtained, with a critical density which depends on the driving force. We also evaluate different characterizations of the ‘distance’ to equilibrium, either dynamic or static: the mass flux, the entropy production rate, the Gibbs free-energy difference between the equilibrium and non-equilibrium stationary states, and the derivative of the non-equilibrium free energy with respect to the applied driving force. The connection between these different non-equilibrium parameters is discussed.